I’m trying to map this entrance:
The specific thing that I’m not sure about how to map is that the entrance is recessed under that overhang. I mapped the overhang as building:part=roof + layer=1, then the footway connected to the back side of the roof (inside the building footprint) with the entrance node. This is what what I have looks like in JOSM:
I don’t think I would do any differently if I’d map this myself.
You even tagged the paths going underneath with covered=yes.
The building:part=* key is from the Simple 3D Buildings (S3DB) tagging standard. To follow that standard, you also need to create an additional building:part=yes area covering the rest of the building. Otherwise, a 3D renderer might (in agreement with the standard) only render that small roof and nothing else of the building.
Noted! Thanks! Out of curiosity, is there a way to accomplish what I want without using building:part?
Sure, you could just use building=roof + layer=1
As @Nadjita said, you could split off those protruding parts of the building and map them with a separat building=roof tag but the building:part - solution is definitely better imho as it reflects the reality.
I am quite sure most people understand such a protruding roof as a part of the complete building in reality and not as a separate building. So the solution you chose is surely the better way imo.
What I would not do is connecting the footways passing under the roof to the outline of the roof (as is at the time being). There is no connection in reality so why should there be one in OSM? Also there is still another service road and a waterway crossing the outline of the building and needing adjustment … so still some work to do there apparently … 
I wouldn’t consider that to be correct mapping. The roof is not a separate building.
Well actually, I would also map it as building:part, but I’d use a building-relation and make sure that the building outlines don’t cover that roof-area. But given that the person asking is likely to be new to the whole theme, I didn’t want to suggest this.
The problem with not using a relation and keeping the roof as building:part is that you’re mapping something that’s not on the ground like if it was covering the ground, which is something I find more incorrect than mapping it as a separate building=roof, but YMMV
